Multi-warehouse package consolidation for split orders in online retailing

Yuankai Zhang, Wei Hua Lin, Minfang Huang, Xiangpei Hu

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


With the rapid growth of the online market in recent years, order splitting has become a great challenge to online retailers for fulfilling multi-item orders in a multi-warehouse storage network. Order splitting can lead to higher shipping costs, the use of more packages, and possible dissatisfaction from customers. This paper presents a multi-warehouse package consolidation approach aimed at consolidating multiple suborders’ stock-keeping units (SKUs) through transshipments among warehouses. A combined multi-commodity network flow model is proposed to determine the consolidation warehouses for each order and make transshipment decisions for individual SKUs. An enhanced logic-based Benders’ decomposition algorithm is proposed to decompose the model into a general multi-commodity network flow master problem and a set of bin packing with conflicts sub-problems. Two proposed Benders’ cuts guarantee the algorithm to converge to optimality. The proposed algorithm can generate the near-optimal result with only about 25% of the CPU time required by CPLEX to solve the proposed model. Numerical experiments reveal that the proposed package consolidation approach outperforms the order splitting fulfillment approach in reducing the total costs, the number of packages, and the delivery times, especially for cases with a small number of SKUs in each suborder which are typical for online retailers. Sensitivity analyses are performed to provide managerial insights of adopting the proposed approach in the real world where order splitting is a common phenomenon.

Original languageEnglish (US)
Pages (from-to)1040-1055
Number of pages16
JournalEuropean Journal of Operational Research
Issue number3
StatePublished - Mar 16 2021


  • Logic-based Benders’ decomposition
  • Logistics
  • Multi-commodity network flow
  • Package consolidation
  • Split order

ASJC Scopus subject areas

  • Computer Science(all)
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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